Prepare for FA2 by studying the six topic areas as one connected system rather than six separate formula lists. Every core technique — firm valuation, capital budgeting, bond pricing, hedging, and performance measurement — depends on matching a cash flow to the discount rate or risk penalty that fits it. Work through the two valuation scenarios, the duration calculation, and the hedge-sizing example below, then run the classification exercise on your own practice questions.
One Discipline Behind All Six FA2 Topic Areas: Matching Cash Flow to Rate
The FA2 topic areas look separate, but they share one rule: every valuation or decision pairs a specific cash flow with the rate that compensates only that cash flow's risk. Build revision around that rule and the syllabus collapses into one map.
Concretely, the pairings look like this: free cash flow to the firm is discounted at the weighted average cost of capital, free cash flow to equity and dividends are discounted at the cost of equity, and a project's cash flows are discounted at a rate reflecting that project's risk, not the firm's average. Fixed income applies the same logic differently — each bond cash flow is discounted at the spot rate for its maturity. Portfolio measurement applies it again: beta-based measures compensate only systematic risk.
Turn this into a working habit. After answering any practice question, write two labels on your rough sheet: which cash flow was used, and which rate or risk measure was used. If the two labels do not correspond — an equity cash flow with a blended rate, a beta penalty applied to a concentrated portfolio — the answer is wrong regardless of how clean the arithmetic was. Keeping a single one-page map of these pairings, updated as you meet new formulas, is more useful than re-reading formula sheets, and you can stress-test it against a question bank such as the free practice set for FA2.
FCFF or FCFE? A Worked Scenario on Picking the Wrong Discount Rate
Value the whole firm with FCFF discounted at WACC; value equity directly with FCFE discounted at the cost of equity. The classic trap is computing one cash flow and discounting it at the other rate, which silently inflates or deflates the result.
Worked scenario (all figures assumed for the exercise): a firm has FCFF of PKR 500 million, interest expense of PKR 100 million, a 30 percent assumed tax rate, net borrowing of PKR 50 million, WACC of 12 percent, cost of equity of 15 percent, and stable growth of 4 percent. FCFE = 500 − 100 × (1 − 0.30) + 50 = PKR 480 million. Equity value via FCFE = 480 / (0.15 − 0.04) ≈ PKR 4,364 million. The plausible mistake: an analyst takes FCFE but discounts it at WACC, giving 480 / (0.12 − 0.04) = PKR 6,000 million. Because WACC is lower than the cost of equity whenever debt is cheaper, this mismatch inflates the equity estimate by roughly 37 percent — shareholders' cash was priced at a blended rate that includes creditors' cheaper capital.
Two checks keep this straight. First, verify the growth assumption fits the denominator: stable growth must stay below the discount rate used, and if near-term growth exceeds it, switch to a two-stage model rather than forcing one terminal division. Second, choose the cash flow by the firm's situation: FCFE works cleanly when leverage is stable and predictable; when leverage is changing or negative FCFE makes equity cash flows erratic, forecast FCFF, discount at WACC to get firm value, then subtract net debt. Practicing the same company both ways, then reconciling the two equity estimates, is the fastest way to internalize the difference.
Capital Budgeting: When NPV and IRR Disagree and the Project Rate Is Not the Firm's WACC
NPV and IRR can rank mutually exclusive projects differently when their scale or cash flow timing differs, and the NPV ranking is the one consistent with value added. The discount rate must reflect the project's risk, not automatically the firm's current WACC.
Worked scenario (assumed figures): at a 10 percent opportunity cost, Project A costs PKR 100 million and returns quickly, with IRR 22 percent and NPV PKR 40 million; Project B costs PKR 300 million with larger, later flows, IRR 17 percent and NPV PKR 95 million. The plausible mistake is selecting A because 22 percent beats 17 percent. IRR is a percentage and ignores scale, and it implicitly assumes interim cash flows are reinvested at the IRR itself — an aggressive assumption when the IRR is high. NPV measures absolute value created at the reinvestment rate equal to the discount rate, so B adds more wealth. The crossover rate — the discount rate at which the two NPV profiles intersect — is what explains the flip: below it, B wins; above it, A wins.
The second trap is applying the firm's average WACC to every project. A company with a 12 percent WACC evaluating a division whose risk profile is materially different should adjust: a riskier-than-average project needs a rate above 12 percent, a safer one below it, whether via a divisional rate, a risk premium, or scenario-based sensitivity analysis. Discounting a risky project at the firm's average rate overstates its NPV, while discounting a safe project at that rate understates it. In practice questions, read the risk description before touching the cash flows, and state in one line why the rate you chose fits that project.
Duration, Modified Duration, and Convexity: Where the Linear Estimate Breaks
Modified duration approximates price change accurately only for small, parallel yield shifts. Convexity captures the curvature, so for large shifts the duration-only estimate drifts, and for callable bonds the relationship can even invert.
Worked scenario (assumed figures): a bond has modified duration 5.8 and convexity 42, and yields fall by 150 basis points. Duration-only estimate: 5.8 × 0.015 = +8.7 percent. Adding convexity: 8.7% + 0.5 × 42 × (0.015)² = 8.7% + 0.47%, so about +9.17 percent. The plausible mistake is reporting 8.7 percent and calling it exact. For plain option-free bonds, convexity is a free benefit — actual gains in a rally exceed the duration estimate and actual losses in a selloff fall short of it — so the linear estimate understates performance in both directions, with the gap growing as the square of the yield change. For immunization work, match the portfolio's Macaulay duration to the horizon, not its maturity; matching maturity leaves the portfolio exposed to reinvestment risk at the horizon date.
Keep the three duration concepts distinct. Macaulay duration is the weighted-average time to cash flows; modified duration is the price sensitivity derived from it; effective (option-adjusted) duration applies when cash flows themselves depend on rates, as with callable or putable bonds. A callable bond can show negative convexity near the call price — its price rises less than duration predicts when yields fall, because the issuer is likely to call. For portfolio-level hedging, money duration or DV01 converts sensitivity into currency units per basis point, which is what a hedge needs to match. Practice stating, for any bond in front of you, which duration applies and why.
Hedging with Futures and Options: Sizing the Position and Choosing the Payoff Shape
A hedge must match the exposure's size, its sensitivity, and the desired payoff shape. Sizing an index futures hedge on notional value alone ignores beta and leaves part of the market exposure unhedged; options reshape the payoff rather than simply offsetting it.
Worked scenario (assumed figures): a PKR 200 million equity portfolio has beta 1.4, and one index futures contract has notional value PKR 5 million. Contracts to short for a full hedge = 1.4 × 200 / 5 = 56. The plausible mistake is shorting 40 contracts — the raw value ratio — which hedges only PKR 200 million of the PKR 280 million beta-weighted exposure and leaves roughly PKR 80 million of market risk live. If the intent is a partial hedge with a target beta, the same formula generalizes: contracts = (target beta − current beta) × portfolio value / futures notional, shorting when the target is lower. Get the sign wrong and the hedge amplifies exposure instead of reducing it.
Options solve a different problem. A protective put sets a floor on the portfolio value at the cost of the premium — full downside protection with upside intact. A covered call generates premium income but caps upside. Shorting futures instead locks in near-current exposure in both directions, sacrificing rally gains for certainty. Distinguish forwards from futures as instruments: forwards are private agreements with settlement at maturity, while futures are exchange-traded and marked to market daily, creating interim cash flow obligations. In scenario questions, first decide whether the goal is to remove exposure, floor it, or monetize a range — then size and pick the instrument.
Sharpe, Treynor, Jensen, and the Information Ratio: One Return History, Four Scorecards
Each performance ratio penalizes a different risk: total volatility (Sharpe), beta (Treynor), expected-return shortfall (Jensen's alpha), or active risk versus a benchmark (information ratio). The portfolio's role — sole holding or diversified sleeve — determines which scorecard applies.
Worked example (assumed figures): Fund P returns 14 percent with volatility 18 percent and beta 0.9; Fund Q returns 13 percent with volatility 12 percent and beta 1.0; the risk-free rate is 8 percent and the benchmark returns 11 percent. Sharpe: P = (14 − 8)/18 ≈ 0.33; Q = (13 − 8)/12 ≈ 0.42, favoring Q. Treynor: P = 6/0.9 ≈ 6.7; Q = 5/1.0 = 5.0, favoring P. Jensen's alpha for P = 14 − [8 + 0.9 × (11 − 8)] = 3.3 percent. The two rankings disagree because P carries diversifiable risk that Treynor ignores; if P is one small sleeve inside a diversified portfolio, its idiosyncratic risk is diluted and Treynor is the fairer lens, while a standalone investor in P should heed the Sharpe result.
Use the information ratio when the question is active management skill rather than absolute return quality: active return divided by tracking error tells you how much excess return was earned per unit of deviation from the benchmark, and it only means anything if the benchmark is the one the mandate actually specifies. Compare ratios only across the same period, the same benchmark, and the same risk definition — a Sharpe from monthly data and a Sharpe from annual data are not directly comparable. In practice questions, the giveaway is the role of the portfolio: sole holding, diversified sleeve, or benchmarked mandate.
| Measure | Risk penalty used | Best suited for | Inputs required |
|---|---|---|---|
| Sharpe ratio | Total standard deviation | Judging a portfolio that is the client's entire holding | Return, risk-free rate, total volatility |
| Treynor ratio | Beta (systematic risk) | Ranking sleeves inside a well-diversified portfolio | Return, risk-free rate, beta |
| Jensen's alpha | Beta via CAPM expected return | Testing whether a manager beat the CAPM-predicted return | Return, benchmark return, risk-free rate, beta |
| Information ratio | Tracking error | Evaluating an active manager against a stated benchmark | Active return, tracking error |
A Four-Week Adaptable Sequence with a Classification Exercise and Readiness Checks
Run an adaptable sequence: week one, build the cash-flow/rate map per topic area; week two, topic drills with a mismatch audit; week three, mixed integrated sets; week four, error-log review and timed practice. Compress or stretch the weeks to fit your calendar.
The core exercise (self-audit): take 15 questions from the free FA2 practice set and, for each, record three labels — cash flow type (firm, equity, project, bond, portfolio), discount rate or risk measure used, and growth or shift assumption. Log every mismatch you discover. Self-check rubric: classify at least 13 of 15 correctly, explain in one sentence why each rate fits its cash flow, and need no more than two formula lookups across the set. If mismatches cluster in one topic area, that area — not the whole syllabus — gets the next drill block, which is how you keep preparation proportionate to your actual gaps rather than spread evenly.
Readiness checks before you sit: reproduce the full pairing map (Section 1) from memory in under ten minutes; complete a duration-plus-convexity calculation cleanly in one pass; size a beta-adjusted futures hedge without hesitating on the sign; state in one sentence why Sharpe and Treynor can rank the same two funds differently; and reconcile an FCFF-based firm value to an FCFE-based equity value on the same company. Self-check scores are learning milestones, not pass predictions. For registration steps, scheduling, and other administrative details, refer to the IFMP website rather than study materials.
References and further reading
Use these references to explore the concepts and check the latest information from the relevant organizations.